Questions on the circle, a curve composed of points that are at a fixed distance from a fixed point.

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3
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1answer
114 views

Find coordinates of intersection between two circles, where one circle is centered on the other

I'm writing a program where an object needs to move from point A to point B. A and B are points on the same circle. Point B corresponds to the intersection between the circle and another circle ...
0
votes
1answer
78 views

Radius of in-circle as a function of the center

I am trying to find the radius of an in-circle in a random triangle as a function of the center of the circle. Let (x,y) in\R^2 be the center of a circle, r the radius then i need an expression of the ...
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3answers
27 views

If $\overline{OQ}\times\overline{OP}=r^2 $ then $\angle OAP=\frac{\pi}{2}$

I would appreciate if somebody could help me with the following problem Q: if $\overline{OQ}\times\overline{OP}=r^2 $ then $\angle OAP=\frac{\pi}{2}$ ($r$: radius of $C$, $C$: circle, $O$: ...
0
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2answers
54 views

Proof Error? A line-segment of a circle is a metric.

In O'searcoid, Metric Spaces, he provides the following example of a metric space: Suppose C is a circle and, for each $a,b ∈ C$, define $d(a,b)$ to be the distance along the line segment from $a$ ...
1
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1answer
405 views

Collision between a circle and a rectangle

I am trying to create a simple model for collisions between a circle and a rectangle to be used in a computer game. The reason I am asking this question here rather than stack overflow is that the ...
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2answers
593 views

What is the area of the shaded region of the square?

To find area of shaded portion in the below figure, the picture generate by following mathematica code. ...
0
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1answer
94 views

Tangent of circumscribed circle

I found a solution online which it said : "It's easy noted that $AG.AE$ = $AD^2$ = $AF^2$ (Using tangent of circumscribed circle)" I found this not obvious at all. I know that $AD = AF$ but why it ...
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2answers
301 views

Does this proof work to prove that the greatest area of a triangle inside a circle is when the triangle is equilateral?

Does this proof work to prove that the greatest area of a triangle inside a circle is when the triangle is equilateral? I gather it doesn't because most of the proofs I've seen use derivatives etc. If ...
0
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1answer
305 views

How to Find the First Moment of Area of a Circular Segment by Integration

Given a segment of circle symmetric about the $y$-axis, I'm wondering how to apply the integral $Q_x = \int y \, dA $ to find the first moment of area with respect to the $x$-axis. I'm having ...
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3answers
1k views

Triangle inscribed in circle, vertex at circle's center, solve for unknown angles.

$O$ is the center of the circle , $A$ and $B$ lie on the circle what are the possible values of $x$ and $y$ I found answers options , asked to mark one or more ...
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2answers
30 views

What is the ratio of the perimeter of $OPRQ$ to the perimeter of $OPSQ$?

Area of circle $O$ is $64\pi$. What is ratio of the perimeter of $OPRQ$ to that of $OPSQ$ ($\pi = 3$)? Okay i have tried couple of things but seems its not working . Please suggest me proper ...
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0answers
79 views

Probability of a certain circular configuration

Pick each of $n$ angles , $\theta_1$ through $\theta_n$ , uniformly randomly in the range $[0,2\pi$]. Define the distance $d_{i,j}$ between $\theta_i$ and $\theta_j$ by $d_{i,j} = \min(|\theta_j - ...
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vote
1answer
2k views

Is there an equation to find the intersection of 3 circles without complex steps?

Is there a way to find the intersection 3 circles without substituting and solving the equations into each other? The reason is because I am making a trilateration program, so I won't really be able ...
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votes
3answers
7k views

Find the equation of a circle given two points and a line that passes through its center

Find the equation of the circle that passes through the points $(0,2)$ and $(6,6)$. Its center is on the line $x-y =1$.
3
votes
1answer
360 views

Do the tangents of two circles define concentric circles?

Given two non-overlapping circles, $R_1$ and $R_2$. The radii of $R_1$ and $R_2$ may be different. The distance between the centers of $R_1$ and $R_2$ is defined as $x$. Draw the four tangents ...
0
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0answers
42 views

Zero cell formed by connecting n random points on a circle by chords

To start, think of a regular n-gon inscribed in a circle. If the vertices of the n-gon are all connected by drawing cords between the other vertices, then another smaller n-gon is created at the ...
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2answers
152 views

Simple question about circumference of circle

Q: The physical education teacher asked to one classroom, by vote, choose a sport between volleyball, basketball and football, to practice in class the following week. pie chart: The segment AB, ...
2
votes
1answer
309 views

Find the area of a circle that is NOT covered by the rectangle

Using the following image for a visual: Is there a formula or equation I can use to find the area of the circle NOT overlapped with the rectangle (i.e. the filled in orange part)? I know all of the ...
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2answers
122 views

Optimum fitting for flanges in a rectangular plate

I have a $2500~\text{mm}\times6300~\text{mm}\times25~\text{mm}$ (width $\times$ length $\times$ thickness) steel plate I want to cut flanges of diameter $235~\text{mm}$ can anyone please suggest $1)$ ...
6
votes
2answers
162 views

Circle Chord Sequence

This is my first post, so be nice! When I was in my first Geometry class in high school, I asked the teacher the following: Given a circle of radius 2a, find the length of the chord running parallel ...
1
vote
1answer
258 views

Intersection of a point and absolute value function contained within a circle

I'm attempting some crazy ideas while programming a game and ran into the following math problem that has been bugging me for a few days: Given a unit circle and a random point $P$ within the circle, ...
2
votes
4answers
207 views

Proof of three points are enough to draw one and only one circle

Using the circle theorems or otherwise, I explained why the process locates the centre of the arc. However, I do not know what 'accuracy limitations of this technique' means. I don't think there is ...
5
votes
4answers
2k views

Newbie: determine if line *segment* intersects circle

I've read related posts, including: How to tell if a line segment intersects with a circle? where the suggestions are probably relevant, but above my level, and the final solution is actually not ...
1
vote
2answers
131 views

Determine counterclockwise moving

in my app, I let user touch and move to draw an arc. After drawing, I got a set of points. Is there any way to determine that user draw the arc counterclockwise or reverse counter clock wise?
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votes
1answer
1k views

What is the area of the shaded part of the circle?

In the diagram below, line segment $AT$ is a diameter of the circle with center $O$. What is the area of the shaded part of the circle? $AT= 16$. Half of the circles area is equal to $100.48$, on ...
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0answers
162 views

family of circles in bipolar coordinate system

I don't get the idea how the equation for this family of curve is $\displaystyle y^2 + (x - a \coth v)^2 = \frac{a^2}{\sinh ^2v}$ from this article on Wikipedia. Suppose, the equation is ...
0
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1answer
156 views

Drawing a triangle in a unit circle

This is a question that I derived for a long time ago. It asks if we draw a triangle in a unit circle does all arc lengths $(\alpha ,\beta ,\theta)$ and sides of triangle $(a,b,c)$ can be rational ...
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2answers
6k views

Determine center of circle if radius and 2 tangent line segments are given

Given the radius and its $2$ tangent lines and their point of intersection of a circle. A similar question is How to calculate the two tangent points to a circle with radius R from two lines given ...
11
votes
6answers
18k views

Area of intersection between two circles

Suppose you have 2 circles that intersect each other in such a way that each circle passes through the other's center. What is the area between the circle(or common area) i.e. area between the centres ...
2
votes
1answer
1k views

A unique circle with 3 points proof

I have prove the theorem: There is only one circle passing through three given non-collinear points in both geometrical and algebraic ways. THere is one question that I just have no idea with. 'the ...
12
votes
1answer
2k views

A hard geometry problem on circles

I found this problem on a website and I couldn't do anything. Do you have any ideas, hints? Edit: If I say $$\frac { { \partial }^{ 2 }f }{ \partial { a }^{ 2 } } +\frac { { \partial }^{ 2 }f }{ ...
3
votes
2answers
92 views

Two questions on clock arithmetic

I have two questions on clock arithmetic, both of which I have solved, but I am looking for neater proofs. Let us suppose we have a circle named $\mathbb{Z}_n$ with $n$ equally spaced points on it ...
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vote
0answers
100 views

Is there a continuous version of $tan^{-1}(\frac{y}{x})$ for the entire unit circle?

The fact that $tan^{-1}(\frac{y}{x})$ only "works" for the upper-right quadrant makes some calculations (for a physics simulator) impossible. I of course use $atan2(y,x)$ in the code, that's not what ...
6
votes
1answer
91 views

Area of circles: represent $x$ in terms of $r_1$ and $r_2$

See the image. Area of green and red regions are equal. Can you represent $x=|O_2D|$ in terms of $r_1$ and $r_2$ for $r_1> r_2$ ? Edit: The point $O_1$ does not enter in the region of small ...
1
vote
1answer
488 views

3D Circle/ground intersection

This one stumps me: A circle in 3D space given by its center = $(0.15, 0.5, 1.0)$, its radius $=64$ and an orientation vector that points away from the circle's plane $(0.251, -0.796, 0.551)$ How ...
0
votes
2answers
59 views

Calculate Point based on distance in 2D-Space

I have a Point P in unit circle (on or in it) with a radius of r. How can I calculate a Point Q with a fixed radius of x, which has the same angle like P
2
votes
3answers
79 views

Drawing dynamic circles based on input value

Is there a formula that will allow me to calculate the radius of a circle based on an input value? The input value could be as small as zero or as large as $10^7$, or larger. The circle is ...
2
votes
1answer
504 views

Circle Packing: Unsolved Problem in Geometry?

Graham and Sloane minimize the second moment of the centres of a number discs in order to maximize their compactness. They use computational geometry techniques to find the optimal packings for ...
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3answers
279 views

Would a circle overlap a parabola's bottom by more than just its vertex?

I mean, out of the condition that a circle actually crosses the parabola. My question is when a circle is "inside" a parabola, would it touch part of the parabola other than just the parabola's vertex ...
2
votes
2answers
182 views

Is the value of $\pi$ in 2d the same in 3d? [closed]

I am starting with my question with the note "Assume no math skills". Given that, all down votes are welcomed. (At the expense of better understanding of course!) Given my first question: What is ...
3
votes
2answers
7k views

What is a perimeter of a sector?

I don't under stand this. So we have: ...
0
votes
1answer
252 views

Ray Disk intersection

So if I have a ray parameterized as $O + tD$ where $O$ is the origin, $D$ is the direction and $t$ is the parameter variable and a flat circular disk with a center point $P$ in 3D space and a radius ...
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1answer
99 views

$\pi$ is just a number, or also the circumference of a sub-unit circle?

A unit circle defined in the Cartesian plane has a radius of $1$ and a diameter of $2$. So making a full round is $2 \pi$. Now, $\pi$ is the ratio of the circumference over the diameter, so if I have ...
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vote
1answer
95 views

Circular motion trig

We have $x_P = -2 + 4 \cos (-\pi t)$ and $y_P = 1 + 4 \sin ( - \pi t)$ with $t$ in seconds. We have to find the coordinates of the intersection with the y-axis. So I use trig and I eventually end up ...
2
votes
0answers
146 views

Ellipse radius interpolation with different radiuses

I am writing a library for graphical LCDs and I want to incorporate a function to draw a circle on the screen. I have already succeeded in drawing simple circles, however, I want to be able to pass a ...
4
votes
4answers
7k views

Relation between chords length and radius of circle

Two chords of a circle, of lengths $2a$ and $2b$ are mutually perpendicular. If the distance of the point at which the chords intersect,from the centre of the circle is $c$($c<$radius of the ...
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vote
1answer
140 views

Are the area of a circle inscribed in a square and the area of the “spandrels” (the four corners that remain) commensurable?

And how would you demonstrate that most simply? See the beginning of my blog post for a little more: http://seekecho.blogspot.fr/2013/02/different-ilks.html
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3answers
483 views

Geometry - Equilateral triangle covered with five circles

I have to cover an equilateral triangle (whose sides are 1m long) with 5 identical circles: what's the minimum radius of the circles?
3
votes
3answers
161 views

Marking the prime points on a circle

If you travel around a circle and mark all the points on the circle where the distance you travelled is a prime number, where you would go through many rotations*, do you end up marking the entire ...
1
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1answer
66 views

Homeomorphism on Identification Space

Let $\sim$ be and equivalence relation on the unit line $X=[0,1]$ defined by $x\sim y$ if either $x=y$ or $\textbf{both}$ $x$ and $y$ $\in$ {${0,\frac{1}{2},1}$}. Construct a homeomorphism ...